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Find value of a and b.
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Given: A square ABCD, with diagonals AC and BD. ∠DEC = (2a-b) ° and ∠ABC = (a+2b) ° 


To find: Value of a and b

Solution:

Both the given angles are 90° 

2a-b = 90 ...............(1)

a+2b = 90 ..............(2)

Multiply the second equation by -2, then add the equations together.


a+2b=90 Becomes −2(a+2b=90)

= −2a−4b=−180

Add these equations to eliminate a:

2a−b=90

−2a−4b=−180

___________

−5b=−90

b=18

Substitute18 for b in 2a−b=90:

We get, 2a−18=90

2a=108

a=54


Answer:

a = 54 and b=18

 

Updated on: 10-Oct-2022

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